IODS Course Project
Justin Box
About the Project
This is Intro to Open Data Science. A course for everyone and a course for anywhere. The course runs for 7 weeks (Tue. 16-18:00) and consists of multiple on-line projects and assignments.
IODS Week 2
This weeks assignments included data wrangling and analysis!
Brief Description of Data
The data in this table is student responses to questions regarding 3 types of learning apporaches (Deep,Surface, and Strategic). The dataset also includes personal characteristics like age, gender. Students were asked several questions (scale 1-5) regarding each type of learning. The average of these responses is presented in the table.
Summary of Results
For this data set, 66% of respondents were female and 34% were male. Their ages ranged from 17-55 (mean 25.5) years old. Points ranged from 7-33 (mean 22.7) The average scale rating of “attitude”“,”deep“,”stra“, and”surf" was 3.1, 3.6, 3.1, and 2.7 respectively
Code
print(students2014) summary(students2014)
Regression Models
Code
library(ggplot2) qplot(attitude, points, data = students2014) + geom_smooth(method = “lm”)
fit a linear model
points_v_attitude <- lm(points ~ attitude, data = students2014)
print out a summary of the model
summary(points_v_attitude)
Interpretation
There is a statistically significant positive correlation between attitude and points (p=4.13e-09).The multiple R-squared value was 0.1906. This means that the strength of the correlation was relatively weak.
Diagnostic Plots
my_model2 <- lm(points ~ attitude + stra, data = students2014)
par(mfrow = c(2,2)) plot(my_model2, which = c(1,2,5))
These diagnostic plots test various aspects of the data such as normality, linearity, and the effect of outliers. These data appear to be normally distributed with a few outliers that could be affecting the linear regression model.
IODS Week 3
The Data
This data evaluates student achievement in secondary education of two Portuguese schools. The data attributes include student grades, demographic, social and school related features and it was collected by using school reports and questionnaires. Two datasets are provided regarding the performance in two distinct subjects: Mathematics (mat) and Portuguese language (por).
For this analysis, the two data sets were combined and only those cases with the same student’s repsonse in BOTH data sets were included.
Description of Variables
For full description of the variables Click Here
alc_use is the average of ‘Dalc’ and ‘Walc’ high_use is TRUE if ‘alc_use’ is higher than 2 and FALSE otherwise
The focus of this analysis is on the relationships between high/low alcohol consumption and selected other variables in the data
My Hypotheses
1) Parental education affects alcohol use
2) Study time affects alcohol use
3) Access to internet affects alcohol use
4) Address affects alcohol use
Analysis
alc <- read.csv(file = “alc.csv”, header=TRUE, sep=“,”)
Looking at Various Plots
##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## Observations: 382
## Variables: 36
## $ X <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
## $ school <fct> GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP,...
## $ sex <fct> F, F, F, F, F, M, M, F, M, M, F, F, M, M, M, F, F, ...
## $ age <int> 18, 17, 15, 15, 16, 16, 16, 17, 15, 15, 15, 15, 15,...
## $ address <fct> U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, ...
## $ famsize <fct> GT3, GT3, LE3, GT3, GT3, LE3, LE3, GT3, LE3, GT3, G...
## $ Pstatus <fct> A, T, T, T, T, T, T, A, A, T, T, T, T, T, A, T, T, ...
## $ Medu <int> 4, 1, 1, 4, 3, 4, 2, 4, 3, 3, 4, 2, 4, 4, 2, 4, 4, ...
## $ Fedu <int> 4, 1, 1, 2, 3, 3, 2, 4, 2, 4, 4, 1, 4, 3, 2, 4, 4, ...
## $ Mjob <fct> at_home, at_home, at_home, health, other, services,...
## $ Fjob <fct> teacher, other, other, services, other, other, othe...
## $ reason <fct> course, course, other, home, home, reputation, home...
## $ nursery <fct> yes, no, yes, yes, yes, yes, yes, yes, yes, yes, ye...
## $ internet <fct> no, yes, yes, yes, no, yes, yes, no, yes, yes, yes,...
## $ guardian <fct> mother, father, mother, mother, father, mother, mot...
## $ traveltime <int> 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, ...
## $ studytime <int> 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, ...
## $ failures <int> 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ schoolsup <fct> yes, no, yes, no, no, no, no, yes, no, no, no, no, ...
## $ famsup <fct> no, yes, no, yes, yes, yes, no, yes, yes, yes, yes,...
## $ paid <fct> no, no, yes, yes, yes, yes, no, no, yes, yes, yes, ...
## $ activities <fct> no, no, no, yes, no, yes, no, no, no, yes, no, yes,...
## $ higher <fct> yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, y...
## $ romantic <fct> no, no, no, yes, no, no, no, no, no, no, no, no, no...
## $ famrel <int> 4, 5, 4, 3, 4, 5, 4, 4, 4, 5, 3, 5, 4, 5, 4, 4, 3, ...
## $ freetime <int> 3, 3, 3, 2, 3, 4, 4, 1, 2, 5, 3, 2, 3, 4, 5, 4, 2, ...
## $ goout <int> 4, 3, 2, 2, 2, 2, 4, 4, 2, 1, 3, 2, 3, 3, 2, 4, 3, ...
## $ Dalc <int> 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
## $ Walc <int> 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1, 3, 2, 1, 2, 2, ...
## $ health <int> 3, 3, 3, 5, 5, 5, 3, 1, 1, 5, 2, 4, 5, 3, 3, 2, 2, ...
## $ absences <int> 5, 3, 8, 1, 2, 8, 0, 4, 0, 0, 1, 2, 1, 1, 0, 5, 8, ...
## $ G1 <int> 2, 7, 10, 14, 8, 14, 12, 8, 16, 13, 12, 10, 13, 11,...
## $ G2 <int> 8, 8, 10, 14, 12, 14, 12, 9, 17, 14, 11, 12, 14, 11...
## $ G3 <int> 8, 8, 11, 14, 12, 14, 12, 10, 18, 14, 12, 12, 13, 1...
## $ alc_use <dbl> 1.0, 1.0, 2.5, 1.0, 1.5, 1.5, 1.0, 1.0, 1.0, 1.0, 1...
## $ high_use <lgl> FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FAL...## Warning: attributes are not identical across measure variables;
## they will be dropped## Observations: 13,752
## Variables: 2
## $ key <chr> "X", "X", "X", "X", "X", "X", "X", "X", "X", "X", "X", "...
## $ value <chr> "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11",...## Warning: attributes are not identical across measure variables;
## they will be dropped
## # A tibble: 4 x 4
## # Groups: sex [?]
## sex high_use count mean_grade
## <fct> <lgl> <int> <dbl>
## 1 F FALSE 156 11.4
## 2 F TRUE 42 11.7
## 3 M FALSE 112 12.2
## 4 M TRUE 72 10.3
Including Plots
## Warning: attributes are not identical across measure variables;
## they will be dropped
Analysis: there appears to be a greater proportion of “high use” individuals who live in rural areas compared to urban.
Analysis: there appears to be a greater proportion of “high use” individuals who studied less than 2 hours per week
Logistic Regression
m <- glm(high_use ~ address + absences + studytime + failures, data = alc, family = “binomial”)
Summary of the Model
# print out a summary of the model
m <- glm(high_use ~ address + absences + studytime + failures, data = alc, family = "binomial")
summary(m)##
## Call:
## glm(formula = high_use ~ address + absences + studytime + failures,
## family = "binomial", data = alc)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3106 -0.8274 -0.6498 1.1066 2.2127
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.03894 0.42264 0.092 0.926596
## addressU -0.49810 0.27809 -1.791 0.073268 .
## absences 0.07883 0.02288 3.446 0.000569 ***
## studytime -0.49431 0.15835 -3.122 0.001798 **
## failures 0.35312 0.19100 1.849 0.064487 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 465.68 on 381 degrees of freedom
## Residual deviance: 426.83 on 377 degrees of freedom
## AIC: 436.83
##
## Number of Fisher Scoring iterations: 4Deviance Residuals: Min 1Q Median 3Q Max
-1.5716 -0.7977 -0.6399 1.1262 2.1197
Coefficients of the Model
## Waiting for profiling to be done...## OR 2.5 % 97.5 %
## (Intercept) 1.0397050 0.4536726 2.3898611
## addressU 0.6076839 0.3532793 1.0542771
## absences 1.0820164 1.0367785 1.1342085
## studytime 0.6099923 0.4431742 0.8256399
## failures 1.4235086 0.9792692 2.0818432An odds ratio (OR) is a measure of association between an exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.
Cross Tabulation
## prediction
## high_use FALSE TRUE
## FALSE 253 15
## TRUE 89 25
## prediction
## high_use FALSE TRUE Sum
## FALSE 0.66230366 0.03926702 0.70157068
## TRUE 0.23298429 0.06544503 0.29842932
## Sum 0.89528796 0.10471204 1.00000000Inaccurately Classified Individuals
## [1] 0.2722513The training error rate here is 27.2%.
Bonus: 10-Fold Cross Validation
## [1] 0.2801047Here the error rate is 28%.
IODS Week 4: Clustering and Classification
About the Data
This week, I investigated the Boston dataset which contains data of housing values in the suburbs of Boston. Boston dataset structure and dimensions are:
str(Boston)## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...dim(Boston)## [1] 506 14All variables are further explained HERE.
Graphing the Data
pairs(Boston, lower.panel = NULL)
This representation is difficult to interpret, so next, I will use a correlation matrix to more easily visualize the data.
cor_matrix<-cor(Boston) %>% round(digits=2)
corrplot(cor_matrix, method="circle", type = "upper", cl.pos = "b", tl.pos = "d", tl.cex = 0.6)
Here, it is much easier to see the correlations. According to this matrix rad (index of accessibility to radial highways) and tax (full-value property-tax rate per $10,000) have the highest positive correlation.
Standardizing the Data
After scaling, the summary of the data is now available:
summary(boston_scaled)## crim zn indus
## Min. :-0.419367 Min. :-0.48724 Min. :-1.5563
## 1st Qu.:-0.410563 1st Qu.:-0.48724 1st Qu.:-0.8668
## Median :-0.390280 Median :-0.48724 Median :-0.2109
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.007389 3rd Qu.: 0.04872 3rd Qu.: 1.0150
## Max. : 9.924110 Max. : 3.80047 Max. : 2.4202
## chas nox rm age
## Min. :-0.2723 Min. :-1.4644 Min. :-3.8764 Min. :-2.3331
## 1st Qu.:-0.2723 1st Qu.:-0.9121 1st Qu.:-0.5681 1st Qu.:-0.8366
## Median :-0.2723 Median :-0.1441 Median :-0.1084 Median : 0.3171
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.:-0.2723 3rd Qu.: 0.5981 3rd Qu.: 0.4823 3rd Qu.: 0.9059
## Max. : 3.6648 Max. : 2.7296 Max. : 3.5515 Max. : 1.1164
## dis rad tax ptratio
## Min. :-1.2658 Min. :-0.9819 Min. :-1.3127 Min. :-2.7047
## 1st Qu.:-0.8049 1st Qu.:-0.6373 1st Qu.:-0.7668 1st Qu.:-0.4876
## Median :-0.2790 Median :-0.5225 Median :-0.4642 Median : 0.2746
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6617 3rd Qu.: 1.6596 3rd Qu.: 1.5294 3rd Qu.: 0.8058
## Max. : 3.9566 Max. : 1.6596 Max. : 1.7964 Max. : 1.6372
## black lstat medv
## Min. :-3.9033 Min. :-1.5296 Min. :-1.9063
## 1st Qu.: 0.2049 1st Qu.:-0.7986 1st Qu.:-0.5989
## Median : 0.3808 Median :-0.1811 Median :-0.1449
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4332 3rd Qu.: 0.6024 3rd Qu.: 0.2683
## Max. : 0.4406 Max. : 3.5453 Max. : 2.9865Now the data is normalized and mean centerd.
Next, I created a categorical variable crime of the crime rate (crim) by using its quantiles as break points. Then, I removed the old crime rate variable (crim) from the dataset and added the new variable crime. This was done with the following R code:
boston_scaled <- as.data.frame(boston_scaled)
bins <- quantile(boston_scaled$crim)
crime <- cut(boston_scaled$crim, breaks = bins, include.lowest = TRUE, label=c("low","med_low","med_high","high"))
boston_scaled <- dplyr::select(boston_scaled, -crim)
boston_scaled <- data.frame(boston_scaled, crime)The final step before performing the Linear Discriminant Analysis (LDA) is to separate the dataset into training (train) and testing (test) sets with a ratio of 4:1.
n <- nrow(boston_scaled)
ind <- sample(n, size = n * 0.8)
train <- boston_scaled[ind,]
test <- boston_scaled[-ind,]Linear Discriminant Analysis
Next, I used the LDA on the training set train. This involves using the categorical crime rate crime as the target variable and all other variables as predictor variables.
lda.fit <- lda(crime ~ ., data = train)
classes <- as.numeric(train$crime)
plot(lda.fit, dimen = 2, col = classes, pch = classes)
Here you can see that the high crime rate grouped more closely than the others.
Making Predictions
First, I saved the crime categories from the test set and then removed the categorical crime variable from the test dataset.
correct_classes <- test$crime
test <- dplyr::select(test, -crime)
lda.pred <- predict(lda.fit, newdata = test)Now I can cross tabulate the results with the crime categories from the test set.
table(correct = correct_classes, predicted = lda.pred$class)## predicted
## correct low med_low med_high high
## low 17 13 1 0
## med_low 3 15 4 0
## med_high 1 8 14 1
## high 0 0 0 25From this table, we can see that the predicitons are fairly accurate depending on the category. In this model, the high was correctly predicted 25 times and incorrectly only 1. Med-high, however, was correctly predicted 14 times and incorrectly 5 times (4 in med_low and 1 in low).
CLusters/Distance Measures
First, the dataset “Boston” has to be re-loaded and re-scaled.
data("Boston")
boston_scaled <- scale(Boston)
boston_scaled <- as.data.frame(boston_scaled)Using the euclidean and manhattan distances, the distance between observations can be measured. Then, a k-means algorithm can be run on the dataset.
km <-kmeans(boston_scaled, centers = 5)
summary(km)## Length Class Mode
## cluster 506 -none- numeric
## centers 70 -none- numeric
## totss 1 -none- numeric
## withinss 5 -none- numeric
## tot.withinss 1 -none- numeric
## betweenss 1 -none- numeric
## size 5 -none- numeric
## iter 1 -none- numeric
## ifault 1 -none- numericFinally, I can investigate the optimal number of clusters then run the algorithm again.
k_max <- 10
twcss <- sapply(1:k_max, function(k){kmeans(boston_scaled, k)$tot.withinss})
qplot(x = 1:k_max, y = twcss, geom = 'line')
It seems that the WCSS decreases significantly between 2-3, so I tried with just 2 clusters.
km <-kmeans(boston_scaled, centers = 2)
pairs(boston_scaled[3:7], col = km$cluster, lower.panel = NULL)
km <-kmeans(boston_scaled, centers = 3)
pairs(boston_scaled[3:7], col = km$cluster, lower.panel = NULL)
With just visual inspection, it appears that 2 clusters appears to be the best option.